Question

A choral conductor has 1774 singers in her choir, some of them are professional singers. The conductor wants to estimate what percentage of singers are professional, but can't ask all 1774, so she instead asks 654 singers in front and finds 30 who are professionals.

a) 4.58%
b) 4.59%
c) 4.60%
d) 4.61%

Answer 1

To estimate the professional singer percentage, the formula (Number of professionals / Total number in the sample) × 100 was used on a sample of 654 singers, with 30 professionals. The correct estimate is 4.59%.

Step-by-step explanation:

The question asks us to estimate the percentage of professional singers in a choir by using a sample. In the sample of 654 singers, 30 were identified as professionals. To find the percentage of professional singers in the sample, we use the formula:

Percentage = (Number of professionals / Total number in the sample) × 100

By plugging in the numbers: Percentage = (30 / 654) × 100, we arrive at an estimated percentage of professional singers in the sample.

When we calculate this, it comes out to be approximately 4.59%. Thus, option b) 4.59% is the correct choice for estimating the percentage of professional singers in the choir based on the sample.